Determine the area of the region between the curves:

f(x) = 2x^2)-29 and g(x) = 2x-5

The area of the region is

Please show me the steps... Thank you!

f(x)=2x²-29

g(x)=2x-5

Lets find intercepts between them.
by setting equal between tem.

2x²-29=2x-5

2x²-2x-24=0

Divide by two both sides.

x²-x-12=0

Factorize

(x-4)(x+3)=0

So they intercept in the points

x=4

x=-3

If you graph this you can see the line 2x-5 is always going to be on the top, so not require to make several integrals, just one is enought.

http://www.wolframalpha.com/input/?i=f%2…

So the area is


. . . . . 4
F(s) = ∫ (top function)-(bottom function) dx
. . . . -3

This is equal to


. . . . . 4
F(s) = ∫ (2x-5)-(2x²-29) dx
. . . . -3


. . . . . 4
F(s) = ∫ (2x-5-2x²+29) dx
. . . . -3

. . . . . 4
F(s) = ∫ (2x-2x²+24) dx
. . . . -3

Integrating.

...................|4
x²-2x³/3+24x.|
...................|-3

The answer is

343/3 u²